Question

若x^2-3x+1=0,求分式x^2/x^4+x^2+1的值

Answer 1

x^2-3x+1=0 两边除以x
x-3+1/x=0
x+1/x=3
x^2/x^4+x^2+1
=1/(x²+1+1/x²)
=1/[(x+1/x)²-1]
=1/(9-1)
=1/8

追问

=1/[(x+1/x)²-1]
=1/(9-1)
=1/8 详细解释

追答

只看分母：x²+1+1/x²
= x²+2+1/x²-1 前面1变成2增加了1 所以应再减去1
=x²+2*x*1/x+1/x²-1 前面是一个完全平方式
=(x+1/x)²-1 前面已算出x+1/x=3 代入进去
=3²-1
=9-1
=8